Space of modular forms of level 1170, weight 2, and Character 1170.cb

• Label: 1170.2.cb
• Level: $1170$
• Weight: $2$
• Character orbit: 1170.cb
• Rep. character: $\chi_{1170}(67,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $336$
• Sturm bound: $504$

Defining parameters

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.cb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 585 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

	Total	New	Old
Modular forms	1040	336	704
Cusp forms	976	336	640
Eisenstein series	64	0	64

Trace form

336 * q - 168 * q^4 + 24 * q^9 - 8 * q^11 - 8 * q^15 - 168 * q^16 - 24 * q^18 - 8 * q^21 - 16 * q^23 + 12 * q^27 + 24 * q^30 - 68 * q^33 + 12 * q^35 - 36 * q^38 + 16 * q^39 - 16 * q^41 + 12 * q^42 + 16 * q^44 + 8 * q^45 + 60 * q^47 - 336 * q^49 - 8 * q^50 - 32 * q^57 - 32 * q^59 - 8 * q^60 - 12 * q^62 + 60 * q^63 + 336 * q^64 + 40 * q^65 - 16 * q^66 - 32 * q^69 - 8 * q^71 + 24 * q^72 - 32 * q^75 - 32 * q^77 - 44 * q^78 - 8 * q^81 + 24 * q^82 + 168 * q^83 + 16 * q^84 - 48 * q^85 - 32 * q^87 + 40 * q^90 + 8 * q^92 + 36 * q^93 - 96 * q^97 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)